The line we are trying to find is perpendicular to y=5, which is a horizontal line.
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The line which is perpendicular (at 90o) to a horizontal line is a vertical line, which would have the equation x=number. SO if we were to put any line which has the general equation x=number, the line should be perpendicular to y=5
Let's try this for x=9:
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As you can, the angle between the two lines is 90o, hence x=9 is perpendicular to y=5
One thing you should notice about any vertical line is that the x-coordinate is always the number that x equals in the equation. So with x=9, all the points will have an x-coordinate of 9.
Since we need the vertical line to go through (−6,1), which has x-coordinate −6, the vertical line equation would be x=−6
If we graph this, it would look like:
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x=−6 is perpendicular to y=5 and also goes through the point (−6,1), so this is your answer.
All lines with the general equation x=number, will not intercept the y-axis, hence they will not have y-intercepts. But, as mentioned before, all points will have an x-coordinate of the number given, so the x-intercept will also be the number given. As the equation of our line is x=−6, the x-intercept is −6.
